The correct answer is 70.95 inches/hour.
To solve this,
The minute hand is rotating at 2pi rad/hour
The hour hand is rotating at 2pi/12 or pi/6 rad/hour
then dα/dt = pi/6 - 2pi = -11pi/6 rad/hour,
α = angle between the two arms
let x - distance between the arms
x^2 = 4^2 + 3^2 - 2(3)(4)cosα
x^2 = 25 - 24cosα
2x(dx/dt) = -24(-sinα)dα/dt
dx/dt = 12(sinα)(dα/dt)/x
4 pm:
α = 120º, sinx = 1/2 and cosα = √/3
x^2 = 25 - 24(√3/2)
x = 2.05314
dx/dt = -12(1/2)(-11pi/6)/2.05314
= -70.95
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